Understanding Functions

algebraic expression

Function Rule: A(n) ________ that defines a function.

slope

The ________ is the number written before the x.

Relation

________: a set of ordered pairs (x, y) where x is the input value and y is the output value.

y intercept

The ________ is the constant written at the end.

Vertical line test

________: a relation is a function if a vertical line does not pass through more than one point on the graph of the relation.

Independent Variable

________: The input of a function (Domain)

3.1

Graphing Relationships

Continuous graph

represent real-world situations that are drawn without any interruptions made up of connected lines or curves

Discrete graphs

are made up of distinct, unconnected points

Domain

Represents all the x values

Range

Represents all the y values

Video Explanation

Graphing Relationships and Interpreting Graphs

3.2

Understanding Relations and Functions

Relation

a set of ordered pairs (x, y) where x is the input value and y is the output value

Function

type of relationship in which there is only one output value for each input value

Vertical line test

a relation is a function if a vertical line does not pass through more than one point on the graph of the relation

Domain

Represents all inputs

Range

Represents all outputs

3.3

Modeling Functions

Independent Variable

The input of a function (Domain)

Dependent variable

The output of a function (Range)

Function notation

If x is the independent variable and y is the dependent variable, then you can use function notation to write y = ƒ(x), which is read "y equals ƒunction of x," where ƒ names the function

Function Rule

An algebraic expression that defines a function

3.4

Graphing Functions

Step 1

Identify and plot the y-intercept

Step 2

Identify the slope and use it to plot the 2nd point